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Contour projected dimension reduction. (English) Zbl 1360.62184

Summary: In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their structural dimensions are no larger than that of the central subspace [R. D. Cook, Regression graphics. Ideas for studying regressions through graphics. New York, NY: Wiley (1998; Zbl 0903.62001)]. Furthermore, we employ CP-sliced inverse regression, CP-sliced average variance estimation and CP-directional regression to estimate the generalized contour subspace, and we subsequently obtain their theoretical properties. Monte Carlo studies demonstrate that the three CP-based dimension reduction methods outperform their corresponding non-CP approaches when the predictors have heavy-tailed elliptical distributions. An empirical example is also presented to illustrate the usefulness of the CP method.

MSC:

62G08 Nonparametric regression and quantile regression
62G35 Nonparametric robustness
62G20 Asymptotic properties of nonparametric inference
62H12 Estimation in multivariate analysis
62J99 Linear inference, regression

Citations:

Zbl 0903.62001

References:

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